Indeed, using
[1]} with \(a=\varepsilon w\)  we have
\(\Vert (f\circ \varphi _{\varepsilon w})^)\Vert _{p,\alpha }^p=\Vert f\circ \varphi _{\varepsilon w}\Vert _{p,\alpha }^p=\) 
\(\int _{\mathbb {D}}|f(z)|^p\frac{(1-|\varepsilon w|^2)^{(2+\alpha )}}{|1-\varepsilon \overline{w} z|^{2(2+\alpha )}}dA_\alpha (z)\le \) 
\(\int _{\mathbb {D}}|f(z)|^p\frac{1}{(1-\varepsilon )^{2(2+\alpha )}}dA_\alpha (z)\le 2^{2(2+\alpha )}\Vert f\Vert _{p,\alpha }^p.\qquad \mathrm {(18)}\) 
